We established an isothermal amplification protocol for DNA/RNA at 50℃ using a thermostable T7 RNA polymerase and 1.4M trehalose. Using this protocol, a natural selection-type evolution reactor for DNA having a {A, T, G} random region was driven. Selected sequences were apt to be AT-rich. Evolution of amplification mechanism from 3SR-scheme to RNA-Z scheme was not observed. The optimum T7 promoter sequence at 50℃ was at the point of Hamming distance 2 from that at 37℃. We also confirmed the quality of DNA libraries for random peptide library of the controlled amino acid composition developed by us (MLSDS method). We studied the evolution dynamics in the evolution reactors using various fitness landscape model. Introducing the evolutionary temperature as a function of mutation rate and population size, we were able to define the free fitness as a Lyapunov function of this process. We could not succeed to integrate all the results into an autonomously evolving molecular entity.